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Simplifying 9(8y2 + -9y + 2) + -6(8y2 + -4y + 8) = 0 Reorder the terms: 9(2 + -9y + 8y2) + -6(8y2 + -4y + 8) = 0 (2 * 9 + -9y * 9 + 8y2 * 9) + -6(8y2 + -4y + 8) = 0 (18 + -81y + 72y2) + -6(8y2 + -4y + 8) = 0 Reorder the terms: 18 + -81y + 72y2 + -6(8 + -4y + 8y2) = 0 18 + -81y + 72y2 + (8 * -6 + -4y * -6 + 8y2 * -6) = 0 18 + -81y + 72y2 + (-48 + 24y + -48y2) = 0 Reorder the terms: 18 + -48 + -81y + 24y + 72y2 + -48y2 = 0 Combine like terms: 18 + -48 = -30 -30 + -81y + 24y + 72y2 + -48y2 = 0 Combine like terms: -81y + 24y = -57y -30 + -57y + 72y2 + -48y2 = 0 Combine like terms: 72y2 + -48y2 = 24y2 -30 + -57y + 24y2 = 0 Solving -30 + -57y + 24y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -19y + 8y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -19y + 8y2)' equal to zero and attempt to solve: Simplifying -10 + -19y + 8y2 = 0 Solving -10 + -19y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -2.375y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.375y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.375y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.375y + y2 = 0 + 1.25 -2.375y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.375y + y2 = 1.25 The y term is -2.375y. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375y + 1.41015625 + y2 = 1.25 + 1.41015625 Reorder the terms: 1.41015625 + -2.375y + y2 = 1.25 + 1.41015625 Combine like terms: 1.25 + 1.41015625 = 2.66015625 1.41015625 + -2.375y + y2 = 2.66015625 Factor a perfect square on the left side: (y + -1.1875)(y + -1.1875) = 2.66015625 Calculate the square root of the right side: 1.630998544 Break this problem into two subproblems by setting (y + -1.1875) equal to 1.630998544 and -1.630998544.Subproblem 1
y + -1.1875 = 1.630998544 Simplifying y + -1.1875 = 1.630998544 Reorder the terms: -1.1875 + y = 1.630998544 Solving -1.1875 + y = 1.630998544 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + y = 1.630998544 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + y = 1.630998544 + 1.1875 y = 1.630998544 + 1.1875 Combine like terms: 1.630998544 + 1.1875 = 2.818498544 y = 2.818498544 Simplifying y = 2.818498544Subproblem 2
y + -1.1875 = -1.630998544 Simplifying y + -1.1875 = -1.630998544 Reorder the terms: -1.1875 + y = -1.630998544 Solving -1.1875 + y = -1.630998544 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + y = -1.630998544 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + y = -1.630998544 + 1.1875 y = -1.630998544 + 1.1875 Combine like terms: -1.630998544 + 1.1875 = -0.443498544 y = -0.443498544 Simplifying y = -0.443498544Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.818498544, -0.443498544}Solution
y = {2.818498544, -0.443498544}
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